Question 1

In testing for the differences between the means of two related populations,you assume that the differences follow a __________ distribution.

Accepted Answer

The answer of In testing for the differences between the...

Question 2

When testing H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is A) 0.0166. B) 0.0332. C) 0.9668. D) 0.9834.

Accepted Answer

The answer of When testing H₀: π₁ - π₂ ≤...

Question 3

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is A) 0.0166. B) 0.0332. C) 0.9668. D) 0.9834.

Accepted Answer

The observed Z test statistic of -2.13 corresponds to a two-tailed test since the alternative hypothesis specifies a not equal to (≠) condition. To find the p-value, we look up the absolute value of the Z score in a standard normal distribution table or use a calculator. The absolute value of -2.13 typically gives a one-tailed p-value around 0.0166. Since it's a two-tailed test, we double this value to get the p-value for both tails, resulting in 0.0332.

Question 4

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,what is the 90% confidence interval estimate for the mean difference in prices?

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 5

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,the p-value for a one-tailed test whose computed statistic is 2.50 (in the hypothesised direction)is between __________ and __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 6

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,there are __________degrees of freedom for this test.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 7

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,the p-value for a two-tailed test whose computed t statistic is 2.50 is between __________ and __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 8

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,what is the 95% confidence interval estimate for the mean difference in prices?

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 9

In testing for the differences between the means of two related populations,the__________ hypothesis is the hypothesis of "no differences".

Accepted Answer

The answer of In testing for the differences between the...

Question 10

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,the calculated value of the test statistic is __________.

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 11

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,a two-tailed test of the null hypothesis of no difference would__________ (be rejected/not be rejecteat the $\alpha$= 0.05 level of significance.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 12

In testing for the differences between the means of two independent populations,you assume that the two populations each follow a__________ distribution.

Accepted Answer

The answer of In testing for the differences between the...

Question 13

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,what is the 99% confidence interval estimate for the mean difference in prices?

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 14

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,if the buyer had decided to perform a two-tailed test,the p-value would have been between __________ and __________.

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 15

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,the pooled (i.e.,combinevariance is __________).

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 16

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,the critical values for a two-tailed test of the null hypothesis of no difference in the population means at the $\alpha$ = 0.05 level of significance are __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 17

Instruction 10-5
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on similar various materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
 $\begin{array}{llll}
\text {Material}&\text {Primary Supplier}&\text {Secondary}&\text {Difference}\
&&\text { Supplier }\ 
1 & \$ 55 & \$ 45 & \$ 10 \
2 & \$ 48 & \$ 47 & \$ 1 \
3 & \$ 31 & \$ 32 & -\$ 1 \
4 & \$ 83 & \$ 77 & \$ 6 \
5 & \$ 37 & \$ 37 & \$ 0 \
6 & \$ 55 & \$ 54 & \$ 1 \
\hline \text { Sum: } & \$ 309 & \$ 292 & \$ 17 \
\text { Sum of Squares: } & \$ 17,573 & \$ 15,472 & \$ 139
\end{array}$

-Referring to Instruction 10-5,the p-value of the test is between __________ and __________.

Accepted Answer

The answer of Instruction 10-5
A buyer for a manufacturing plant...

Question 18

When testing H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is A) 0.0166. B) 0.0332. C) 0.9668. D) 0.9834.

Accepted Answer

A negative Z value corresponds to a lower tail area of the standard normal distribution. Using a standard normal distribution table or calculator, the area to the left of -2.13 is approximately 0.0166. Therefore, the p-value for this test is 0.0166, which is less than the significance level of 0.05. This means we reject the null hypothesis H₀: π₁ - π₂ ≥ 0 in favor of the alternative hypothesis H₁: π₁ - π₂ < 0.

Question 19

Instruction 10-6
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
-Referring to Instruction 10-6,the computed t statistic is __________.

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Question 20

Instruction 10-6 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. -Referring to Instruction 10-6,if you were interested in testing against the one-tailed alternative that $\mu$₁ > $\mu$₂ at the$\alpha$ = 0.01 level of significance,the null hypothesis would __________ .

Accepted Answer

The answer of Instruction 10-6
Two samples each of size 25...

Quiz 10: Hypothesis Testing: Two-Sample Tests

In testing for the differences between the means of two related populations,you assume that the differences follow a __________ distribution.

When testing H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

When testing H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

In testing for the differences between the means of two related populations,the__________ hypothesis is the hypothesis of "no differences".

In testing for the differences between the means of two independent populations,you assume that the two populations each follow a__________ distribution.

When testing H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

When testing H₀: π₁ - π₂ ≤ 0 versus H₁: π₁ - π₂ > 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

When testing H₀: π₁ - π₂ = 0 versus H₁: π₁ - π₂ ≠ 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is

When testing H₀: π₁ - π₂ ≥ 0 versus H₁: π₁ - π₂ < 0,the observed value of the Z test statistic was found to be -2.13.The p-value for this test is